Recent advances in cyber-physical systems, artificial intelligence, and cloud computing have driven the wide deployment of Internet-of-things (IoT) in smart homes. As IoT devices often directly interact with the users and environments, this paper studies if and how we could explore the collective insights from multiple heterogeneous IoT devices to infer user activities for home safety monitoring and assisted living. Specifically, we develop a new system, namely IoTMosaic, to first profile diverse user activities with distinct IoT device event sequences, which are extracted from smart home network traffic based on their TCP/IP data packet signatures. Given the challenges of missing and out-of-order IoT device events due to device malfunctions or varying network and system latencies, IoTMosaic further develops simple yet effective approximate matching algorithms to identify user activities from real-world IoT network traffic. Our experimental results on thousands of user activities in the smart home environment over two months show that our proposed algorithms can infer different user activities from IoT network traffic in smart homes with the overall accuracy, precision, and recall of 0.99, 0.99, and 1.00, respectively.